This course is an introduction into formal concept analysis (FCA), a mathematical theory oriented at applications in knowledge representation, knowledge acquisition, data analysis and visualization. It provides tools for understanding the data by representing it as a hierarchy of concepts or, more exactly, a concept lattice. FCA can help in processing a wide class of data types providing a framework in which various data analysis and knowledge acquisition techniques can be formulated. In this course, we focus on some of these techniques, as well as cover the theoretical foundations and algorithmic issues of FCA.
Upon completion of the course, the students will be able to use the mathematical techniques and computational tools of formal concept analysis in their own research projects involving data processing. Among other things, the students will learn about FCA-based approaches to clustering and dependency mining.
The course is self-contained, although basic knowledge of elementary set theory, propositional logic, and probability theory would help.
End-of-the-week quizzes include easy questions aimed at checking basic understanding of the topic, as well as more advanced problems that may require some effort to be solved.

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Working with real data

A concept lattice can be exponentially large in the size of its formal context. Sometimes this can be due to noise in data. We'll study a few heuristics to filter out noisy concepts or select the most interesting concepts in a large lattice built from real data: stability and separation indices, concept probability, iceberg lattices. We will also talk about association rules, which is a name for implications that are supported by strong evidence, but may still have counterexamples in data.